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MATHEMATICAL ANALYSIS I

CODE 72290
ACADEMIC YEAR 2021/2022
CREDITS
  • 12 cfu during the 1st year of 8715 INGEGNERIA CIVILE E AMBIENTALE (L-7) - GENOVA
  • 12 cfu during the 1st year of 8722 INGEGNERIA NAVALE (L-9) - GENOVA
  • SCIENTIFIC DISCIPLINARY SECTOR MAT/05
    LANGUAGE Italian
    TEACHING LOCATION
  • GENOVA
  • SEMESTER Annual
    PREREQUISITES
    Prerequisites (for future units)
    This unit is a prerequisite for:
    • Civil and Environmental Engineering 8715 (coorte 2021/2022)
    • PROBABILISTIC METHODS FOR CIVIL AND ENVIRONMENTAL ENGINEERING 104396
    • HYDRAULICS 60397
    • GEOMATHICS 84520
    • GEOTECHNICS 99062
    • MATHEMATICAL ANALYSIS II 60243
    • STRUCTURAL MECHANICS II 66285
    • MATHEMATICAL PHYSICS 60354
    • APPLIED PHYSICS 60356
    • HYDROLOGY & HYDRAULIC URBAN INFRASTRUCTURES 66097
    • STRUCTURAL MECHANICS I 72506
    • STRUCTURAL ENGINEERING I 72543
    • URBAN PLANNING AND TRANSPORTATION ENGINEERING 84522
    • Naval Architecture and Marine Engineering 8722 (coorte 2021/2022)
    • APPLIED PHYSICS 60361
    • RATIONAL MECHANICS 60143
    • AUTOMATIC CONTROL FOR NAVAL ENGINEERING 66048
    • STRUCTURAL MECHANICS AND HYDRODYNAMICS 66281
    • MATHEMATICAL ANALYSIS II AND GEOMETRY 2 86966
    TEACHING MATERIALS AULAWEB

    OVERVIEW

    The lectures are delivered in Italian.

    This is a full year course. Between the first and the second semester there will be a break, during which no lectures will be delivered.

    The first semester will be devoted to limits and differential calculus for functions of one real variable, while in the second semester integral calculus in one variable, functions of two variables and an introduction to differential equations will be dealt with.

    AIMS AND CONTENT

    LEARNING OUTCOMES

    Capability in following a line of logical reasoning; understanding of the essential properties of differential and integral calculus for functions of one variable, differential equations and functions of several variables. Acquisition of a sufficient calculation ability.

    AIMS AND LEARNING OUTCOMES

    The main objective is to supply the fundamentals of differential and integral calculus in one variable, differential equations and functions of several variables: these are some fundamental instruments in Mathematical Analysis,  essential to get a well grounded knowledge in the basic branches of Mathematics and for the understanding of simultaneous and next courses.

    Expected learning outcomes:

    The students will become acquainted with the concepts and proofs carried out in class and how they are used in practice to solve exercises; moreover they will know how to produce easy examples on topics covered in this course.

    In particular, students are expected to develop the following skills: operations on limits and derivatives, study of functions of one variable, integral calculus (indefinite, definite and improper integrals), study of integral functions, elementary study of level curves of functions of two varlables, resolution of simple differential equations of first order, resolution of linear differential equations of order n with constant coefficients.

    PREREQUISITES

    Numerical Sets, equations and inequalities, powers properties, analytical geometry, trigonometry

    TEACHING METHODS

    Lectures (120 hours).

    Both theory and exercises are presented by the teachers in the classroom on the blackboard. Moreover some tutorial exercitations will be carried out during the semester.

    SYLLABUS/CONTENT

    Real numbers, cartesian coordinates in a plane, functions of one real variable, monotonic functions, composition and invertibility of functions, elementary functions, supremum and infimum, limits of functions, limits of sequences, infinitesimal and infinite functions, continuous functions and their properties, derivatives, derivation rules, derivatives of elementary functions, sign of derivatives in the study of monotonicity and convexity, maxima and minima, theorems of Fermat, Rolle, Lagrange, de l'Hospital, Taylor expansions and applications to critical points, definite and indefinite integrals, fundamental theorem of integral calculus, integral functions, improper integrals, real functions of two variables (domain, limits at a point and at infinity, continuity, partial and directional derivatives, differentiability and tangent plane, maxima and minima), linear first order differential equations with continuous coefficients, linear differential equations of order n with constant coefficients, separation of variables.

    RECOMMENDED READING/BIBLIOGRAPHY

    C.Trapani. Analisi matematica: Funzioni di una variabile reale, McGraw-Hill (2008)

    M. Bramanti, C. Pagani, S. Salsa. Analisi Matematica 1, Zanichelli (2008)

    M. Bertsch, R. Dal Passo. Elementi di analisi matematica, Aracne (2000)

    M. Baronti, F. De Mari, R. Van der Putten, I. Venturi. Calculus problems, Springer (2016)

    TEACHERS AND EXAM BOARD

    Exam Board

    CRISTINA CAMPI (President)

    MICHELE PIANA

    ELISABETTA VALLARINO (President Substitute)

    LESSONS

    Class schedule

    All class schedules are posted on the EasyAcademy portal.

    EXAMS

    EXAM DESCRIPTION

    The exam consists of a written and an oral test. In order to access to the oral test, the student will be required of an evaluation of at least 15/30. Oral test has to be taken in the same exam appeal of written test.

    Furthermore, during the year, there will be two partial written tests. The students that will pass them (that is, obtaining in each partial test an evaluation of at least 15/30), will be enabled to access directly the oral exam; this is valid for all the exam appeals for the academic year, hence until February included.

    ASSESSMENT METHODS

    The written examination consists in some exercises about the topics covered in this course. In such a test is proven the ability to solve problems relating to calculation of limits, derivatives and integrals of one variable functions, study of properties of one or more variables functions and ordinary differential equations.

    The test lasts two hours and it is possible to consult the notes and textbooks; the same procedures apply to each of the two partial written tests.

    In the oral exam a discussion of the written examination is done; moreover some questions are asked on the course content and/or about the solution of some exercises about the topics covered in this course. In such way they are assessed the understanding and the knowledge of the concepts and reasoning skills acquired by the students.

    Exam schedule

    Date Time Location Type Notes
    20/12/2021 09:00 GENOVA Scritto + Orale
    20/12/2021 15:00 GENOVA Scritto + Orale
    03/02/2022 09:00 GENOVA Scritto Appello riservato agli studenti della coorte 2020/21 e precedenti. Cambio orario: l'esame inizierà alle ore 11:30
    04/02/2022 09:00 GENOVA Orale Appello riservato agli studenti della coorte 2020/21 e precedenti.
    06/06/2022 14:00 GENOVA Compitino
    10/06/2022 09:00 GENOVA Scritto
    15/06/2022 09:00 GENOVA Orale
    11/07/2022 09:00 GENOVA Scritto
    18/07/2022 09:00 GENOVA Orale
    05/09/2022 09:00 GENOVA Scritto
    09/09/2022 09:00 GENOVA Orale

    FURTHER INFORMATION

    Attendance is recommended.

    Students are suggested to enroll in AulaWeb, in order to be able to get further information by the teachers about the course.